# Investigation 6: Galaxy Clusters - Activity 3

## Applying Doppler Effect to Moving Galaxies

Overview: Students make the observation that farther galaxies move away faster, and check that a model of an expanding universe makes predictions that match with those observations.

Physical resources: Expanding universe model

Electronic resources: Virtual spectroscopy

Observations of moving galaxies:

• Motivating question: How can we use the idea of redshift to figure out the velocity of objects? Students brainstorm ideas with group.
• How do we know what was emitted? Introduce spectral lines as the photon we know must have been emitted with a certain energy, in our case, we'll look at line emission from hydrogen atoms.
• Virtual spectroscope activity: (MiniSpectroscopy
• Examine Hydrogen spectrum at rest, predict how "example galaxy" is moving, relative to Earth. (Peak is at a longer wavelength, so it is moving away from us.)
• Give students only the spectra of galaxies A through D
• What direction are they moving? (away from Earth, because peak of emission is at a longer wavelength than it is when hydrogen is at rest)
• Challenge: put them in order by the speed (slowest to fastest) they are moving away from Earth.
• Now, give students the images of galaxies A through D
• What's different about these galaxies? (angular diameter)
• Given that most galaxies are about the same linear diameter, put them in order by their distance from Earth, closest to furthest.
• Students should describe the pattern in these observations, and put their description on the whiteboard. (The order is the same, further galaxies move away faster.)
• Instructor introduces Hubble's law as a restatement of this observation: Galaxies that are farther away move away from us faster.

Model of expanding universe, to explain Hubble's law observations above:

• Introduce two-dimensional "expanding universe" model which we've taken an image of at two different times
• Label "smaller" universe as time t = 0, and "larger" universe as time t = 10 seconds.
• Have groups of students "live" in galaxy A, B or C and have them make predictions of the following for each of the two other labeled galaxies, as well as another galaxy of their choice:
• Distance from your galaxy to other galaxy at time t = 0 seconds (cm)
• Distance from your galaxy to other galaxy at time t = 10 seconds (cm)
• Change in distance (cm)
• Change in time (sec, all should be 10 seconds)
• Speed = change in distance / change in time (cm / sec)
• Direction of motion (description, or arrow)
• Have students populate classroom prediction table
• Discussion:
• Summarize important patterns seen in predictions: Galaxies at a greater distance move faster.
• Have students line up their "home galaxy" while holding both "universes" up to the light, and describe what has happened to all the other galaxies (they have moved away from the home galaxy, on a line connecting the home galaxy to the other galaxy.) Then have them switch their "Home galaxy" to the other two labeled galaxies, in turn. (All galaxies will see this pattern of all others moving away).
• Refined prediction: Galaxies at a greater distance move faster, and move away from each other along a line connecting the two. From any galaxy, all others look like they are moving away.
• These predictions match up with the observations we've made about actual galaxies in our universe, so we can't rule out the "expanding universe" model.

Teacher tips/tricks:

• Some students have difficulty identifying what information they should extract from the spectra when comparing the sample of galaxies. They may think the intensity of the peak is what they should order by, instead of the location of the peak on the wavelength (energy) scale.
• Many students have difficulty separating the observations from the models in this activity. If so, clarify with the assessment question below.

Assessment ideas:

• Can we determine redshifts for galaxies that do not have emission lines? (no, we must know the energy at which the photons were originally emitted).
• What if we observed every galaxy moving toward us, with further galaxies moving toward us faster? How would that change our model to explain the observations? (contracting universe).
• Which is a statement of the Doppler effect, and which is a statement of Hubble's Law?
• When we observe galaxies moving away from us, we receive lower energy photons compared to what that galaxy actually emits. (Doppler effect)
• Galaxies moving away from us faster are also further away (Hubble's Law).
• Galaxies moving towards us give us photons that are higher energy than when they were emitted (Doppler effect).
• Closer galaxies are moving away from us slower (Hubble's Law).
• Discuss what each deals with: Hubble's law relates speed to distance, and Doppler effect relates change in energy of photons to speed of motion.
• Image of review page of notes: (Hubble's law 2)

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